I thought I had sent an answer to Paul Taylor's question, but - since I have not seen it on the bulletin board - I suppose I slipped up somewhere in transmitting it. Anyway, as Ross Street has pointed out in his message of today, the whole matter was discussed in detail in my old paper "Mono- morphisms, epimorphisms, and pull-backs", J.Austral. Math. Soc. 9(1969),124-142 - which contains some interesting results, besides being couched in the generality that Paul seeks. Were I writing it today, I should change it in places; certainly, I should speak of ARBITRARY intersections of monos, or of strong monos, or of regular monos, rather than of SMALL intersections coupled with WELLPOWEREDNESS. There are good things in Freyd-Kelly, "Categories of continuous functors I", J.Pure Appl. Algebra 2(1972),169-191,but we chose there to speak not of STRONG epis but of EXTREMAL ones, these coin- ciding under our hypotheses there. In several later papers I have refined various points from that very early paper - but it contains the guts of the matter. Max Kelly, 21 Feb. =========================================================================